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Three-leg four-wire inverters are expected to play an essential role in power distribution because of its ability to handle the neutral current caused by unbalanced or non-linear loads. This paper presents a comprehensive analysis for a novel three-dimensional space vector modulation (3-D-SVMI) algorithm for three-leg four-wire inverters. A zero vector is generated by turning off all power switches to produce zero volts at the output terminals of the inverter. In this paper, the topology for the inverter is analyzed. Further, switching vectors, separation planes, the matrices for switching vectors duty cycles and the switching sequences are derived. Simulation results for different load conditions are shown to validate the proposed approach.